Quick 'n' easy question about doppler effect

Am I right when I say that the doppler effect formula "f=f0((v+vo)/(v+vs))" is derivated from the classical theorem of speed addition and this is why the doppler effect for light and EM waves is different?

I don't get how on this page: hyperphysics they get the first equation... I don't see the relativistic doppler effect written that way anywhere and I don't understand how they get ot that equation and how to expand it with maple...Anybody can help?

Staff: Mentor

That equation is just the relativistic Doppler formula rewritten in a form convenient for deriving the low speed approximation. They took something that usually appears in a form like:
[tex]\sqrt{\frac{1 + x}{1 - x}}[/tex]
And rewrote it like:
[tex]\frac{\sqrt{1 - x^2}}{1 - x}[/tex]
These expressions are equivalent.